Details

sample517.0ms

Algorithm

intervals

Results

262.0ms	105×	body	1280	valid
138.0ms	59×	body	640	valid
18.0ms	24×	body	320	valid
11.0ms	60×	body	80	valid
4.0ms	8×	body	160	valid

simplify34.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	21
5	21
4	20
3	18
2	16
1	12
0	8

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.7b

localize48.0ms

Local error

Found 3 expressions with local error:

0.2b	(* r (/ (sin b) (cos (+ a b))))
0.2b	(/ (sin b) (cos (+ a b)))
2.8b	(cos (+ a b))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
19×	`*-un-lft-identity` `times-frac` `add-cube-cbrt`
13×	`associate-r`
10×	`add-cbrt-cube` `add-exp-log`
5×	`pow1`
3×	`associate-/r` `associate-l` `insert-posit16` `associate-/l` `add-log-exp`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
1×	`cos-sum` `clear-num` `frac-2neg` `pow-prod-down` `associate-r/` `-commutative`

Counts

3 → 70

Calls

3 calls:

25.0ms	(* r (/ (sin b) (cos (+ a b))))
18.0ms	(/ (sin b) (cos (+ a b)))
17.0ms	(cos (+ a b))

series506.0ms

Counts

3 → 9

Calls

3 calls:

269.0ms	(* r (/ (sin b) (cos (+ a b))))
108.0ms	(/ (sin b) (cos (+ a b)))
128.0ms	(cos (+ a b))

simplify1.1s

Counts

79 → 79

Iterations

Iter	Nodes
done	2008
3	2008
2	844
1	271
0	120

prune881.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.2b

localize31.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
0.2b	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
0.2b	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
0.2b	(* (sin a) (sin b))

rewrite154.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
22×	`*-un-lft-identity` `add-cube-cbrt`
20×	`associate-r`
19×	`times-frac`
13×	`add-cbrt-cube` `add-exp-log`
8×	`pow1` `associate-/r/`
7×	`sin-mult`
6×	`associate-l` `cos-mult` `add-log-exp`
4×	`insert-posit16`
3×	`associate-/r` `flip3--` `prod-exp` `frac-sub` `cbrt-unprod` `flip--` `associate-/l` `sub-div` `unswap-sqr`
2×	`cbrt-undiv` `div-exp` `pow-prod-down` `*-commutative` `div-inv`
1×	`clear-num` `sub-neg` `frac-2neg` `diff-log` `associate-*r/`

Counts

4 → 104

Calls

4 calls:

34.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
83.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
24.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
11.0ms	(* (sin a) (sin b))

series690.0ms

Counts

4 → 12

Calls

4 calls:

123.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
326.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
167.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
73.0ms	(* (sin a) (sin b))

simplify1.3s

Counts

116 → 116

Iterations

Iter	Nodes
done	2016
3	2016
2	1478
1	439
0	175

prune1.6s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize36.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
0.1b	(* r (sin b))
0.2b	(* (sin a) (sin b))
0.3b	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

rewrite135.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
13×	`add-cbrt-cube` `add-exp-log`
10×	`*-un-lft-identity` `add-cube-cbrt`
8×	`pow1`
6×	`associate-r` `associate-l` `add-log-exp`
5×	`sin-mult`
4×	`associate-/r/` `cos-mult` `insert-posit16`
3×	`associate-/r*` `times-frac` `prod-exp` `cbrt-unprod`
2×	`cbrt-undiv` `flip3--` `div-exp` `pow-prod-down` `*-commutative` `frac-sub` `flip--` `sub-div` `unswap-sqr`
1×	`clear-num` `sub-neg` `frac-2neg` `diff-log` `div-inv` `associate-/l*`

Counts

4 → 80

Calls

4 calls:

33.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
17.0ms	(* r (sin b))
23.0ms	(* (sin a) (sin b))
61.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series577.0ms

Counts

4 → 12

Calls

4 calls:

131.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
52.0ms	(* r (sin b))
69.0ms	(* (sin a) (sin b))
324.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify1.4s

Counts

92 → 92

Iterations

Iter	Nodes
done	2164
3	2164
2	1237
1	365
0	145

prune1.4s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize38.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin a) (sin b))
0.3b	(/ (* r (sin b)) (- (* (cos a) (cos b)) (cbrt (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (sin a) (sin b))))))
0.3b	(* (* (sin a) (sin b)) (* (sin a) (sin b)))
26.1b	(cbrt (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (sin a) (sin b))))

rewrite360.0ms

Algorithm

rewrite-expression-head

Rules

45×	`pow1`
29×	`sin-mult`
23×	`add-cbrt-cube` `add-exp-log`
18×	`pow-prod-down`
14×	`cbrt-div`
11×	`frac-times` `associate-*l/`
10×	`add-sqr-sqrt` `prod-exp` `cbrt-unprod`
9×	`associate-/r/`
8×	`*-un-lft-identity` `add-cube-cbrt`
7×	`associate-*r/` `cos-mult` `frac-sub`
4×	`associate-r` `associate-l` `pow-sqr` `pow-prod-up` `insert-posit16` `add-log-exp`
3×	`associate-/r*` `times-frac`
2×	`cbrt-undiv` `pow-plus` `div-exp` `*-commutative`
1×	`cbrt-prod` `pow2` `clear-num` `frac-2neg` `flip3--` `pow1/3` `swap-sqr` `pow3` `rem-cbrt-cube` `div-inv` `flip--` `associate-/l*` `unswap-sqr`

Counts

4 → 107

Calls

4 calls:

22.0ms	(* (sin a) (sin b))
143.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (cbrt (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (sin a) (sin b))))))
85.0ms	(* (* (sin a) (sin b)) (* (sin a) (sin b)))
107.0ms	(cbrt (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (sin a) (sin b))))

series552.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(* (sin a) (sin b))
328.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (cbrt (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (sin a) (sin b))))))
72.0ms	(* (* (sin a) (sin b)) (* (sin a) (sin b)))
86.0ms	(cbrt (* (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (sin a) (sin b))))

simplify1.3s

Counts

119 → 119

Iterations

Iter	Nodes
done	2000
3	2000
2	1739
1	513
0	202

prune2.0s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

regimes355.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	19
1	19
0	15

end0.0ms

sample7.5s

Algorithm

intervals

Results

4.4s	2947×	body	1280	valid
1.7s	1870×	body	640	valid
476.0ms	742×	body	320	valid
467.0ms	2117×	body	80	valid
156.0ms	325×	body	160	valid